Two-point function of strangeness-carrying vector-currents in two-loop Chiral Perturbation Theory

TL;DR

This paper computes the two-loop correlator of strangeness-carrying vector currents in chiral perturbation theory, providing a finite, scale-independent expression useful for low energy theorems and phenomenological parameter determination.

Contribution

It presents the first two-loop renormalized, finite, and scale-independent calculation of the vector-current correlator with strangeness in chiral perturbation theory.

Findings

Derived a two-loop finite energy sum rule for $Q_V$.

Provided a scale-independent, renormalized correlator expression.

Enhanced precision in determining flavor-breaking vector current parameters.

Abstract

We calculate the correlator between two external vector-currents having the quantum-numbers of a charged kaon. We give the renormalized expression to two loops in standard chiral perturbation theory in the isospin limit, which, as a physical result, is finite and scale-independent. Applications include a low energy theorem, valid at two loop order, of a flavor breaking combination of vector current correlators as well as a determination of the phenomenologically relevant finite $O(p^6)$-counterterm combination $Q_V$ by means of inverse moment finite energy sum rules. This determination is less sensitive to isospin-breaking effects than previous attempts.